Yeah system capacity is an issue. So if you are running a lot of demand with remote start, available power is diverted away from the battery and to the aux systems. Considering that the car is really idling when remote started, and that the max alternator output doesn't happen until AFTER 2,000+ rpm (or 75-80 mph). You would need to put in a rebuilt alternator that raises the entire curve, I would say 1/3 to 1/2. And that is a LOT.
For a 2007 Edge, for example
78/143 amp (max) @ 620-2500 engine rpm @ normal engine temperature